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Question
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Solution
Given (4x − 5y) (16x2 + 20xy + 25y2)
We shall use the identity `(a-b)(a^2 + ab + b^2) = a^3 -b^3`
We can rearrange the (4x − 5y) (16x2 + 20xy + 25y2)as
` =(4x - 5y)[(4x)^2 + (4x)(5y) + (5y)^2]`
` = (4x)^3 - (5y)^3`
` = (4x) xx (4x) xx (4x) + (5y) xx (5y) xx (5y)`
` = 64x^3 - 125y^2`
Hence the Product value of ` (3x+2y)(9x^2 - 6xy + 4y^2)`is `64x^3 - 125y^3`.
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